On a new multivariate IFR ageing notion based on the standard construction

Abstract

Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the classical univariate convex transform order. A new multivariate generalization of the convex transform order has recently been proposed in the literature. In this work, we propose a new multivariate IFR notion for multivariate distributions based on comparisons in this new order with a properly defined exponentially distributed random vector. Properties, applications, and illustrations of this new notion are given as well.